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Gelfand–Tornheim theorem

Theorem.

The normed fieldmeans a field KKK having a subfieldRRR isomorphic to ℝℝ\mathbb{R} and satisfying the following:
There is a mapping∥⋅∥fragmentsparallel-tonormal-⋅parallel-to\|\cdot\| from KKK to the set of non-negativereals such that